7 papers
Persistent Homology and Equivariance in Data Analysis: A Topological Introduction
Patrizio Frosini, Ulderico Fugacci, Nicola Quercioli +1
This new book is intended as a first elementary introduction to Topological Data Analysis for mathematics students seeking a rigorous account of the foundations of persistent homol…
LARAG: Link-Aware Retrieval Strategy for RAG Systems in Hyperlinked Technical Documentation
Giorgia Bolognesi, Claudio Estatico, Ulderico Fugacci +3
Retrieval-Augmented Generation (RAG) enhances the factual grounding of Large Language Models by conditioning their outputs on external documents. However, standard embedding-based…
Hook-decomposable modules and their resolutions
Isabella Mastroianni, Marco Guerra, Ulderico Fugacci +1
We compare several classes of biparameter persistence modules: -products of monoparameter modules, hook-decomposable modules, modules admitting a Smith-type structure theorem,…
The Convex Matching Distance in Multiparameter Persistence
Francesco Conti, Patrizio Frosini, Ulderico Fugacci +4
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the pe…
Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules
Isabella Mastroianni, Marco Guerra, Ulderico Fugacci +1
Motivated by the need to relate the biparameter persistence module induced by a pair of scalar functions with the monoparameter persistence modules induced by each function separat…
SHREC 2025: Protein surface shape retrieval including electrostatic potential
Taher Yacoub, Camille Depenveiller, Atsushi Tatsuma +25
This SHREC 2025 track dedicated to protein surface shape retrieval involved 9 participating teams. We evaluated the performance in retrieval of 15 proposed methods on a large datas…